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Solution of systems of linear equations by the use of punched card equipment

Solution of Systems of Linear Equations
by the Use of Punched Card Equipment
1. Introduction
A set of equations such as
2x * 3y « 3 2 equations
6x - y • 4 2 unimeims
0!*
3K # 4y .♦ ds * 16 3 equations
03c • 3y -*-»«* 5 3 unknowns
»4x + y « s » 89
or sots containing more. equations and sore unknowns are called
systems of linear squat ions* The solution of such a system of
equations consists in finding a sot of values* one for each of
tli® unknown variables, that will cause each equation to be
satisfied* In order that there be on® and only one such sol -
tion (or set of values) for the problem it is usual to require
that the number of unknowns and the number of equations foe equal,
IS shall tacitly asanas that our systems of equations are of
this kind altho the method we shall give can he applied to find
the solution of any system Insofar as such solutions exist*
fhe solution of such linear systems occurs as part of the
solution of many practical problems* Each correlation requires
such a solution, and asany other amplications are found in
statistics* Blectrleal circuit analysis and/ the analysis of
structures are two engineering fields requiring the frequent
solution of large linear systems of equations*
The exact or approximate solution of linear ordinary and
0485

Solution of Systems of Linear Equations
by the Use of Punched Card Equipment
1. Introduction
A set of equations such as
2x * 3y « 3 2 equations
6x - y • 4 2 unimeims
0!*
3K # 4y .♦ ds * 16 3 equations
03c • 3y -*-»«* 5 3 unknowns
»4x + y « s » 89
or sots containing more. equations and sore unknowns are called
systems of linear squat ions* The solution of such a system of
equations consists in finding a sot of values* one for each of
tli® unknown variables, that will cause each equation to be
satisfied* In order that there be on® and only one such sol -
tion (or set of values) for the problem it is usual to require
that the number of unknowns and the number of equations foe equal,
IS shall tacitly asanas that our systems of equations are of
this kind altho the method we shall give can he applied to find
the solution of any system Insofar as such solutions exist*
fhe solution of such linear systems occurs as part of the
solution of many practical problems* Each correlation requires
such a solution, and asany other amplications are found in
statistics* Blectrleal circuit analysis and/ the analysis of
structures are two engineering fields requiring the frequent
solution of large linear systems of equations*
The exact or approximate solution of linear ordinary and
0485